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if slope of one of the lines given by ax 2+2hxy+by 2=0 is three times the other then the condition for h is

if slope of one of the lines given by ax 2+2hxy+by 2=0 is three times the other then the condition for h is
 

Grade:12

1 Answers

Aakanksha Talreja
34 Points
6 years ago
divide d given equation by x^{2} and let y/x be slope m hence we get bm^{2}+2hm+a=0
nw, let d roots of this equation bem_{1} , m_{2} as given m_{1} =3 m_{2} nw SOR = m1 + m2=-2h/b=4m2
POR=m1m2=3 m_{2}^{2} = a/b therefore, m_{2}=\sqrt{a/3b} , m_{2}=\sqrt{a/3b}= - h/2b \therefore h=-2\sqrt{ab/3}

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